Interpreting CUSUM graphs

To interpret the CUSUM graph one needs to look at the slope of the graph, and specifically where slope changes occur. A constant slope is an indication of a stable value in the underlying data despite the presence of noise. In the example given earlier, a number of relatively "constant" slope areas can be identified, and these are shown superimposed on the graph. Points at which the slope changes are the turning points and these have been denoted with vertical lines.

So what do you do with the turning points? We'll this gives you an indication of where to average values from. In the example given, the first identified period is from t=1..14s, and the average for this period is 1.0. For the second period t=15..30s, the average is 6.4, and so on. I haven't shown this but you you could add this graphically to the bottom series as straight lines between the turning points for clarity, at the appropriate y-axis average value.

There is some danger in identifying too many turning points, as you could start reading something into the data which just isn't there. The greater the change in slope, the more convincing the turning point. In this example the turning points near 48, 72 and 84 are the most convincing.

To assist in calculating the average from the graph, one can add a calibration scale/mask which shows the relationship between set slopes and average values. We'll save details on how to do that for a later post though.

Introducing the CUSUM chart

The Cumulative Sum chart (CUSUM) is a very useful (and powerful) tool to pick up small changes in trends of noisy data- and it works just as well if there are large trend changes. Despite what some might say, it is actually relatively easy to apply this technique in a spreadsheet to analyse your data, although one must understand how to interpret the graph.

The CUSUM is very useful to identify important dates or times (turning points) where a trend change occurred, especially where one finds that this is not obvious when looking at the time series data.
You can use it to guage the likelihood that other noisy variables could be causes if one can pick up similar trend changes in these variables. It finds applications in data analysis especially of process data and is a tool that can be used by Six Sigma practitioners.

In my next post I will elaborate on how to implement this useful technique in a spreadsheet such as Excel or OpenOffice, and also show an example, and more importantly how to interpret the graph, so stay tuned. For now, here are some related links.

Cusum Link 1 (NIST)
Cusum Link 2 (iSixSigma)